"Had the Reviewer's object, in this instance, been to discover the truth, or had he known how to pursue it, it is perfectly clear, at first sight, that he would not have instituted a comparison between the prolificness which exists in the small towns he has alluded to, and that in certain districts, the population of which is made up, partly of rural inhabitants and partly of accumulations of people in immense masses, the prolificness of which, if he will allow me still the use of the phrase, is inversely as their magnitude; but he would have compared these small towns with the country places properly so called, and then again the different classes of towns with each other; this method would have led him to certain conclusions on the subject."

Now, this reply shows that Mr. Sadler does not in the least understand the principle which he has himself laid down. What is that principle? It is this, that the fecundity of human beings on given spaces, varies inversely as their numbers. We know what he means by inverse variation. But we must suppose that he uses the words, "given spaces" in the proper sense. Given spaces are equal spaces. Is there any reason to believe, that in those parts of Surrey which lie within the bills of mortality there is any space, equal in area to the space on which Guildford stands, which is more thickly peopled than the space on which Guildford stands? We do not know that there is any such. We are sure that there are not many. Why, therefore, on Mr. Sadler's principle, should the people of Guildford be more prolific than the people who live within the bills of mortality? And, if the people of Guildford ought, as on Mr. Sadler's principle they unquestionably ought, to stand as low in the scale of fecundity as the people of Southwark itself, it follows, most clearly, that they ought to stand far lower than the average obtained by taking all the people of Surrey together.

The same remark applies to the case of Birming

ham, and to all the other cases which Mr. Sadler mentions. Towns of 5000 inhabitants may be, and often are, as thickly peopled, "on a given space," as Birmingham. They are, in other words, as thickly peopled as a portion of Birmingham, equal to them If so, on Mr. Sadler's principle, they ought to be as low in the scale of fecundity as Birmingham. But they are not so. On the contrary, they stand higher than the average obtained by taking the fecundity of Birmingham in combination with the fecundity of the rural districts of Warwickshire.

in area.

The plain fact is, that Mr. Sadler has confounded the population of a city with its population “on a given space," a mistake which, in a gentleman who assures us that mathematical science was one of his early and favourite studies, is somewhat curious. It is as absurd, on his principle, to say that the fecundity of London ought to be less than the fecundity of Edinburgh, because London has a greater population than Edinburgh, as to say that the fecundity of Russia ought to be greater than that of England, because Russia has a greater population than England. He cannot say that the spaces on which towns stand are too small to exemplify the truth of his principle. For he has himself brought forward the scale of fecundity in towns, as a proof of his. principle. And, in the very passage which we quoted above, he tells us that, if we knew how to pursue truth, or wished to find it, we "should have compared these small towns with country places, and the different classes of towns with each other." That is to say, we ought to compare together such unequal spaces as give results favourable to his theory, and never to compare such equal spaces as give results opposed to it. Does he mean

any thing by "a given space?" a given space?" Or does he mean merely such a space as suits his argument? It is perfectly clear that, if he is allowed to take this course, he may prove any thing. No fact can come amiss to him. Suppose, for example, that the fecundity of New York should prove to be smaller than the fecundity of Liverpool. "That," says Mr. Sadler, "makes for my theory. For there are more people within two miles of the Broadway of New York, than within two miles of the Exchange of Liverpool." Suppose, on the other hand, that the fecundity of New York should be greater than the fecundity of Liverpool. "This," says Mr. Sadler again," is an unanswerable proof of my theory. For there are many more people within forty miles of Liverpool than within forty miles of New York." In order to obtain his numbers, he takes spaces in any combinations which may suit him. In order to obtain his averages, he takes numbers in any combinations which may suit him. And then he tells us that, because his tables, at the first glance, look well for his theory, his theory is irrefragably proved.

We will add a few words respecting the argument which we drew from the peerage. Mr. Sadler asserted that the Peers were a class condemned by nature to sterility. We denied this, and showed, from the last edition of Debrett, that the Peers of the United King„dom have considerably more than the average number of children to a marriage. Mr. Sadler's answer has amused us much. He denies the accuracy of our counting, and, by reckoning all the Scotch and Irish Peers as Peers of the United Kingdom, certainly makes very different numbers from those which we gave. A member of the Parliament of the United Kingdom might have been expected, we think, to

know better what a Peer of the United Kingdom

is.

By taking the Scotch and Irish Peers, Mr. Sadler has altered the average. But it is considerably higher than the average fecundity of England, and still, therefore, constitutes an unanswerable argument against his theory.

The shifts to which, in this difficulty, he has re› course, are exceedingly diverting. "The average fecundity of the marriages of Peers," said we, "is higher by one-fifth than the average fecundity of marriages throughout the kingdom."

"Where, or by whom did the Reviewer find it supposed," answers Mr. Sadler, "that the registered baptisms expressed the full fecundity of the marriages of England?"

But

Assuredly, if the registers of England are so defective as to explain the difference which, on our calculation, exists between the fecundity of the peers and the fecundity of the people, no argument against Mr. Sadler's theory can be drawn from that difference. what becomes of all the other arguments which Mr. Sadler has founded on these very registers? Above all, what becomes of his comparison between the censuses of England and France? In the pamphlet before us, he dwells with great complacency on a coincidence which seems to him to support his theory, and which to us seems, of itself, sufficient to overthrow it.

In my table of the population of France, in the forty-four departments in which there are from one to two hectares to each inhabitant, the fecundity of 100 marriages, calculated on the average of the results of the three computations relating to different periods given in my table, is 4067. In the twenty-two counties of England, in which there is from one to two hectares to each inhabitant, or

from 129 to 259 on the square mile, beginning, therefore, with Huntingdonshire, and ending with Worcestershire, - the whole number of marriages during ten years will be found to amount to 379,624, and the whole number of the births during the same term to 1,545,549 or 4071 births to 100 marriages! A difference of one in one thousand only, compared with the French proportion!"

ΤΟ

Does not Mr. Sadler see that, if the registers of England, which are notoriously very defective, give a result exactly corresponding almost to an unit with that obtained from the registers of France, which are notoriously very full and accurate, this proves the very reverse of what he employs it to prove? The correspondence of the registers proves that there is no correspondence in the facts. In order to raise the average fecundity of England even to the level of the average fecundity of the peers of the three kingdoms, which is 3.81 to a marriage, it is necessary to add nearly six per cent. to the number of births given in the English registers. But, if this addition be made, we shall have, in the counties of England, from Huntingdonshire to Worcestershire inclusive, 4:30 births to a marriage or thereabouts; and the boasted coincidence between the phenomena of propagation in France and England disappears at once. This is a curious specimen of Mr. Sadler's proficiency in the art of making excuses. In the same pamphlet he reasons as if the same registers were accurate to one in a thousand, and as if they were wrong at the very least by one in eighteen.

He tries to show that we have not taken a fair criterion of the fecundity of the peers. We are not quite sure that we understand his reasoning on this subject. The order of his observations is more than usually зonfused, and the cloud of words more than usually